X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Fgeneral%2Fdel2.m;fp=octave_packages%2Fm%2Fgeneral%2Fdel2.m;h=f3972e28fb4397b38af27acbd778c66456c0305e;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278

diff --git a/octave_packages/m/general/del2.m b/octave_packages/m/general/del2.m
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+## Copyright (C) 2000-2012 Kai Habel
+## Copyright (C) 2007  David Bateman
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {@var{d} =} del2 (@var{M})
+## @deftypefnx {Function File} {@var{d} =} del2 (@var{M}, @var{h})
+## @deftypefnx {Function File} {@var{d} =} del2 (@var{M}, @var{dx}, @var{dy}, @dots{})
+##
+## Calculate the discrete Laplace
+## @tex
+## operator $( \nabla^2 )$.
+## @end tex
+## @ifnottex
+## operator.
+## @end ifnottex
+## For a 2-dimensional matrix @var{M} this is defined as
+## @tex
+## $$d = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+##       1    / d^2            d^2         \
+## D  = --- * | ---  M(x,y) +  ---  M(x,y) |
+##       4    \ dx^2           dy^2        /
+## @end group
+## @end example
+##
+## @end ifnottex
+## For N-dimensional arrays the sum in parentheses is expanded to include second
+## derivatives over the additional higher dimensions.
+##
+## The spacing between evaluation points may be defined by @var{h}, which is a
+## scalar defining the equidistant spacing in all dimensions.  Alternatively,
+## the spacing in each dimension may be defined separately by @var{dx},
+## @var{dy}, etc.  A scalar spacing argument defines equidistant spacing,
+## whereas a vector argument can be used to specify variable spacing.  The
+## length of the spacing vectors must match the respective dimension of
+## @var{M}.  The default spacing value is 1.
+##
+## At least 3 data points are needed for each dimension.  Boundary points are
+## calculated from the linear extrapolation of interior points.
+##
+## @seealso{gradient, diff}
+## @end deftypefn
+
+## Author:  Kai Habel <kai.habel@gmx.de>
+
+function D = del2 (M, varargin)
+
+  if (nargin < 1)
+    print_usage ();
+  endif
+
+  nd = ndims (M);
+  sz = size (M);
+  dx = cell (1, nd);
+  if (nargin == 2 || nargin == 1)
+    if (nargin == 1)
+      h = 1;
+    else
+      h = varargin{1};
+    endif
+    for i = 1 : nd
+      if (isscalar (h))
+        dx{i} = h * ones (sz (i), 1);
+      else
+        if (length (h) == sz (i))
+          dx{i} = diff (h)(:);
+        else
+          error ("del2: dimensionality mismatch in %d-th spacing vector", i);
+        endif
+      endif
+    endfor
+  elseif (nargin - 1 == nd)
+    ## Reverse dx{1} and dx{2} as the X-dim is the 2nd dim of the ND array
+    tmp = varargin{1};
+    varargin{1} = varargin{2};
+    varargin{2} = tmp;
+
+    for i = 1 : nd
+      if (isscalar (varargin{i}))
+        dx{i} = varargin{i} * ones (sz (i), 1);
+      else
+        if (length (varargin{i}) == sz (i))
+          dx{i} = diff (varargin{i})(:);
+        else
+          error ("del2: dimensionality mismatch in %d-th spacing vector", i);
+        endif
+      endif
+    endfor
+  else
+    print_usage ();
+  endif
+
+  idx = cell (1, nd);
+  for i = 1: nd
+    idx{i} = ":";
+  endfor
+
+  D = zeros (sz);
+  for i = 1: nd
+    if (sz(i) >= 3)
+      DD = zeros (sz);
+      idx1 = idx2 = idx3 = idx;
+
+      ## interior points
+      idx1{i} = 1 : sz(i) - 2;
+      idx2{i} = 2 : sz(i) - 1;
+      idx3{i} = 3 : sz(i);
+      szi = sz;
+      szi (i) = 1;
+
+      h1 = repmat (shiftdim (dx{i}(1 : sz(i) - 2), 1 - i), szi);
+      h2 = repmat (shiftdim (dx{i}(2 : sz(i) - 1), 1 - i), szi);
+      DD(idx2{:}) = ((M(idx1{:}) - M(idx2{:})) ./ h1 + ...
+                     (M(idx3{:}) - M(idx2{:})) ./ h2) ./ (h1 + h2);
+
+      ## left and right boundary
+      if (sz(i) == 3)
+        DD(idx1{:}) = DD(idx3{:}) = DD(idx2{:});
+      else
+        idx1{i} = 1;
+        idx2{i} = 2;
+        idx3{i} = 3;
+        DD(idx1{:}) = (dx{i}(1) + dx{i}(2)) / dx{i}(2) * DD (idx2{:}) - ...
+            dx{i}(1) / dx{i}(2) * DD (idx3{:});
+
+        idx1{i} = sz(i);
+        idx2{i} = sz(i) - 1;
+        idx3{i} = sz(i) - 2;
+        DD(idx1{:}) =  (dx{i}(sz(i) - 1) + dx{i}(sz(i) - 2)) / ...
+            dx{i}(sz(i) - 2) * DD (idx2{:}) - ...
+            dx{i}(sz(i) - 1) / dx{i}(sz(i) - 2) * DD (idx3{:});
+      endif
+
+      D += DD;
+    endif
+  endfor
+
+  D = D ./ nd;
+endfunction